Mathematical Society of Japan Memoirs

Symmetric functions and the Yangian decomposition of the Fock and basic modules of the affine Lie algebra $\hat{\mathfrak{s}\mathfrak{l}}_{N}$

Denis Uglov

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Abstract

The decomposition of the Fock and basic modules of the affine Lie algebra $\mathfrak{sl}_{N}$ into irreducible submodules of the Yangian $Y(\mathfrak{gl}_N$ is constructed. Each of the irreducible submodules admits the unique up to normalization eigenbasis of the maximal commutative subalgebra of the Yangian. The elements of this eigenbasis are identified with specializations of Macdonald symmetric functions where both parameters of the latter approach an Nth primitive root of unity.

Chapter information

Source
Ivan Cherednik, Peter J. Forrester and Denis Uglov, Quantum Many-Body Problems and Representation Theory (Tokyo: The Mathematical Society of Japan, 1998), 183-241

Dates
First available in Project Euclid: 17 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.msjm/1389985795

Digital Object Identifier
doi:10.2969/msjmemoirs/00101C030

Mathematical Reviews number (MathSciNet)
MR1724950

Zentralblatt MATH identifier
1053.05120

Rights
Copyright © 1998, The Mathematical Society of Japan

Citation

Uglov, Denis. Symmetric functions and the Yangian decomposition of the Fock and basic modules of the affine Lie algebra $\hat{\mathfrak{s}\mathfrak{l}}_{N}$. Quantum Many-Body Problems and Representation Theory, 183--241, The Mathematical Society of Japan, Tokyo, Japan, 1998. doi:10.2969/msjmemoirs/00101C030. https://projecteuclid.org/euclid.msjm/1389985795


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